Research

Interests

My research interests include optimization under uncertainty and Bayesian inverse problems. I’m also interested in combining operator learning and uncertainty quantification for scientific and engineering applications.

Hybrid Infinite-dimensional Spherical-radial Decomposition (hiSRD) for Chance-constrained Optimizations

In this joint work with my advisor Georg Stadler, we develop hybrid infinite-dimensional spherical-radial decomposition (hiSRD), which combines SRD on a finite-dimensional subspace with Monte Carlo sampling of the infinite-dimensional remainder. The method eliminates truncation bias while keeping variance reduction and differentiability, enabling unbiased estimates of joint chance-constraint probability functions and their gradients. We also show theoretically how the variance advantage of finite-dimensional SRD deteriorates as the stochastic dimension grows and demonstrate hiSRD in PDE-constrained optimal control and chance-constrained Gaussian process regression, where it ensures accurate probability and gradient estimates for optimization.